OK you guys, thanks for thinking that I'm not smart enough to have looked for a way to remove the screen.
My screen door is latched shut by the two sliding bolts on the left side of the door, one at the top, and the other at the bottom.
Here are 6 thumbnails and click throughs to full size pics of the exterior side and interior side of the door.
As you can see, there are no angle pieces that are screwed to the inside of the door frame to hold the screen in place. I do not see any removable pieces anywhere on the door. All I see are Aircraft rivets on the exterior and pop rivets on the interior.
So, does anyone have a suggestion as to how my screen gets replaced, other than to tear the whole interior skin off?